-L920
A bigger version of the 925
A bit dated? Would a 3 year old phone still be good? Can be had for $200 or less

Then there's the new 830 and 730 but those are a bit pricey.

If there are other phones feel free to list them. The phone needs to have LTE and 8.1.

Right off the bat I'm going to say that these phones are all about the same in terms of performance.
I personally doubt the battery life of the 920, 925 will be up-to-snuff. I heard the 1020's is better. But I don't know firsthand.

The 920 and 925 are almost identical (besides the obvious and some minor things), and the 1020 isn't too different. I wouldn't be concerned with the age gap between the 925 and 920 since they're pretty darn close.

My wife has a 925 and it is outstanding. The only problem is the 16GB of internal memory. If you can get buy with that amount of storage I would highly recommend it. If you can get it for 200$ or less go for it. I was hoping the 735 would be out in the US by now and sell for around 250$. If it was that is what I would get. But it is not. The 830 is nice; but its not worth 449$ at least not to me.